Have you ever tried to envision the shape that a plate will take under load?
Being able to do so
is important for understanding how plates work.
It is also important
for identifying regions with high curvature and moment,
and points of maximum deflection.
We designed this model
to help students better understand plate deflection.
Let's use it to investigate a square plate
with simple supports,
as indicated by these dashed lines.
The white grid makes it easy to see the shape
that the plate will take as it is loaded.
As you can see,
the curvature is positive like a smile,
everywhere, and in both directions.
You can also see that the maximum deflection
occurs at the center of the plate.
If we now clamp one of the edges
(denoted by the solid line),
we discover a negative moment (like a frown)
along the clamped edge.
The same thing would happen
if one end of a beam
were changed from a simple support
to a clamped support.
A simply-supported plate that spans two bays
takes this shape,
and it exhibits both positive and negative curvatures.
If we remove the center support,
we get a rectangular plate,
and it takes this shape under load.
Notice how the curvature across the width of the plate
remains nearly constant until you get near its ends.
Notice, too, that the curvature in the long direction
is nearly zero except near the ends.
If we remove one of the end supports,
the plate deflects like this,
and removing the other end support,
produces this result.
Notice how bending occurs in only one direction.
If a slab is curved in only one direction,
the load must be carried entirely
by stresses in that direction,
and it is called a one-way slab.
If the supports caused a plate
to curve in both directions,
we have a two-way slab.
Carrying of the load is then shared
by stresses in the two directions,
and deflection is reduced.
Floors in buildings are often supported by columns.
as, in this model system.
As you can see,
the deflection pattern is quite different
from that of a plate
that is supported along its edges.
And here is a column-supported plate
that spans two bays.
Suppose we had a floor with an overhang.
How do you think it would deform?
Here is what the model shows us.
Just for fun, here is one more design we can build with the model.
Can you understand why the plate takes the shape it does?
Understanding plate curvature is especially important
in the design of concrete floor slabs.
The reason is that concrete --
like the blocks in this model --
cannot be relied on to carry tension.
Consequently, steel reinforcing must be incorporated
any place that tension could arise.
And that includes the tension side
of any regions where bending occurs.
That is why it is important to know
the direction and degree of bending
at every point in a plate.
You might be wondering about the weigh scales
that are part of the plate bending kit.
They allow you to investigate how load is transferred
to supporting columns
and beams.
They can also help you to understand tributary areas,
a topic we don't have time to discuss here.
Thanks for watching!